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Isn't this programming-related? Could maybe find some answers on stackoverflow.
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FarinhaAug 26 '10 at 19:55

Request Tracker also known as RT supports emailing bugs and replying via email. It does support retrieving the email with full headers, but seems to mangle formatting in a web view. It does not allow you to reply to the original email sent, instead a reply must be sent with the ticket number in the subject line.

At work, we use a commercial product called OnTime for bug tracking. It is primarily a Windows application, but it does also have a web component.

It has the ability to receive emails directly as bugs into the database and to send an auto-acknowledgement email in response. You can also reply to the emails from within the software (including as HTML emails), and also include attachments. All email conversations done this way are associated with the bug item.

It is a bit clunky to use, but it does keep an audit trail of the communication about a bug.

At work we use OnTime, but in the past we have also used FogBugz. I found FogBugz to be easier to use.
OnTime has a free 1 user licence if you want to try it out. FogBugz also has a free trial (for 45 days)
We have also used Kayako in-house, but I haven't had much exposure to it to say if it any good or not. They also have a free trial.